Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in the table below.
Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in the table below.
Table: Forward/backward Sway (in mm) of Elderly Subjects
| 19 | 30 | 20 | 19 | 29 | 25 | 21 | 24 | 50 |
Set up and run a test of hypothesis to determine if the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Use a level of significance of 5%. Specifically, do the following:
(i) Write down the null and alternative hypotheses.
(ii) Verify that the assumptions necessary to apply the test are satisfied.
(iii) What is the test statistic and what is the p-value?
(iv) State your conclusion.
